. Utl-c, Yu -div(e(r,A) Vr) : f (r,A,t)

. Dans-le-cadre-du-groupe-de-travail-momas, pour le stockage souterrain des déchets nucléaires, on essaie de résoudre Ie cas test Couplexl à I'aide des schémas boîte. On résoud l'équation de Darcy à I'aide d'un schéma boîte étudié sur des maillages en triangles. La résolution de l'écorrlement cles nr:cléides dans le sol est faite par !e schéma boîte ADL Ce tra, ail en ccurs est réalisé par J-M. Sac Epée qui réécrit en C++, les codes matlab des schémas boîte pour la rapidité de I'exécution

. Parallélement, il sera intéressant de développer un schéma boîte plus précis, du type pschéma

. Schéma-de-boîte, augmentation de r9:0.505, pp.2-2

. Compa, raison schéma boîte (1.37) et p-schéma boîte (1.7S) p -l, T : 2.10-2

A. Décentrement, Du : 0. On observe des oscillations dispersives, LTS

]. A. Bibliographie1, C. Bellcunn, J. A. Counn, V. Lôenz, and . Mlnrtfinz, A Finite Volume Method with a Modified ENO Scheme using a Hermite Interpolation to solve Advection- Diffusion Equations, Int. J. Numer. Meth. Engng, vol.50, pp.2339-237, 2001.

I. Bnsu5re, Error bounds for finite elements method, Numer.Math

F. Bnnzzt and R. A. , On the existence, uniqueness and approximation of saddle point problems, arising from Lagrangian multipliers, pp.322-333

D. I4l and . Bnenss, Finite Elements, 1997.

F. Bnnzzt, J. Douclas, and L. D. Menini, Two families of Mixed Finite Element for second order elliptic problems, Numer. Math, vol.47, pp.2-7, 1985.

S. Brnnner-sr and S. Scott, The mathematical Theory of the Finite Element Method, 1994.

C. Bpnnardr, C. Cenuto, and Y. M. , Generalized inf-sup conditions for Chebyshev spectral approximation of the Stokes problem, SIAM J. Numer.4nal, vol.256, pp.237-264, 1988.

J. J. Cnetror, Box-schemes for First Order Partial Differential Equations, Advaaces in Comp. Fluid Dynamics, pp.307-331, 1995.

J. J. Cu and S. Lrror, Met,sr, A "box-scheme" for the Euler equations, Lecture Notes in Math, vol.1270, pp.82-99, 1987.

[. Cuou and S. Tnnc, Comparing two approaches of analizing mixed finite volume methods, J. KSIAM,S, vol.1, pp.55-78, 2001.

S. Chou, D. Y. Kwax, and K. Y. Ktm, Mixed finite volume methods on nonstaggered quadrilateral grids for elliptic problems, Mathematics of Computation, vol.72, issue.242
DOI : 10.1090/S0025-5718-02-01426-6

B. Counser, Schémas à deux points pour la simulation numérique des écoulements, pp.2-46, 1990.

B. Counsnr, Etude d'une famille de schémas boîte à deux points et application à la dynamique des gaz monodimensionnelle, pp.3-44, 1991.

B. Cournur, Schémas boîte en réseau triangulaire, p.992

B. Cournnr and J. P. , CRolsll,ln, Finite Volume Box Schemes on triangular meshes, Math. Model. and Num er, vol.325, pp.631-649, 1998.

J. Cnorsrlle, Finite Volume Box Schemes and Mixed Methods, Math. Model. and Numer, vol.34, issue.5, pp.1087-1106, 2000.

J. Cnolsrlle, Keller's box-scheme for the one-dimensional stationary convectiondiffusion equation, CoUPUTING, pp.37-63, 2002.

J. Cnorsrlle, Un schéma boîte pour l'équation de convection-diffusion stationnaire !d, Préprint de I'Ilniversité de Met2, 2003.

J. Crolsrlle and I. , GRutr'r, Some box-schemes for elliptic problems, Nurnerica] M+ thods for Partial Differential Bquations, pp.355-373, 2001.

J. Crorsrlle and I. Gnprf, A box scheme for convection-diffusion equations, Proc of the 3, 2002.

[. Cnolsrlle and I. Gnprf, A box scheme for convection-diffusion equations with sharp contrast in the diffusion coefficients

M. Cnovzutx, P. Rrvnrr, and R. A. , Conforming and nonconforming finite element methods , for solving the stationary Stokes equations I, pp.33-76, 1973.

M. Cnouzurx, P-A. Ravrenr Introduction à I'analyse numérique des équations aux dérivées partielles

J. Doucles and J. E. Gutttt, A general formulation of alternating direction methods; Part I. Parabolic and hyperbolic problems, pp.428-453

2. J. Doucr and H. H. Racuford, On the numerical solution of heat conduction pro blems in two and three space variables. Tnens, oF THE AMER, pp.42-439, 1956.

A. N. Doucl, . Annoln, R. S. Borrl, and K. Fat, Approximation by quadrilateral finite elements, Mathematics of computation, vol.71, issue.239, pp.909-922, 2002.

W. Hecxeuscu, On first and second order box schemes, Computing, pp.277-296, 1989.

M. Fonrrn and M. Soulte, A non-conforming piecewise quadratic finite element on triangles, Int. J. Num. meth. Etg, vol.19, pp.505-520, 1983.

M. Fonrrn and M. Flnrloui, A non-conforming mixed finite element for second order elliptic problems, 1997.

M. Inons and A. Rtzzaeun, Experience with the patch test for convergence of finite element, The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations, pp.557-588

R. Crnpnntrer, A. De-la-bounoonnaye, and B. Lennoururou, On the derivation of the modified equation for the analysis of linear numerical methods, Math. Model. and Numer, vol.37, issue.4, pp.459-470, 1997.

J. É. Mnrrrp, About a "natural" mixed finite element method;relation with classical methods and applications. Talk at the ENUMATH 99, 1999.

3. B. Novn and H. H. Tan, Finite difierence methods for solving the 2D convectiondiffusion equation, Int. Jour. Numer. Meth. Flu, issue.9, pp.75-98, 1989.

W. Ppecnuen and H. Rnchford, The numerical solution of parabolic and elliptic differential equations, Journal of the Society for Industrial and Applied Mathematics, vol.3, pp.28-32, 1955.

R. Rauxecher and S. Turnx, Simple Nonconforming Quadrilateral Stokes Element, Numer. Meth. Partial Ditr. Equations, vol.8, pp.97-111, 1992.

P. Revrrrr and J. Tuouas, A mixed finite element method for 2nd order elliptic problems, Lecture Notes in Math, vol.606, pp.292-295

J. Srrrxwerda, Finite Difference Schemes and Partial Differential Equations, 1989.

G. Srnang and G. Frx, An analysis of the Finite Element Method, 1973.

L. Srynps and . Tostsxn, The streamline-diffusion method for nonconforming tht elements on rectangular tensor-product meshes, IMA Journal of Numerical Analysis, vol.2, pp.21-42, 2001.

S. L. Tnuscort and I. W. Tunnpr, An investigation of Spatial and Temporal Weighting Schemes for use in Unstructured Mesh Control Volume Finite Element Methods, 10th Comp. Tech. App. Conf, 2001.

S. F. Wonnou, Application of compact difference schemes to the conservative Euler equations for one-dimensional flows, NASA Teeh. Mem, vol.83262, 1982.

F. Wonnom and M. M. Hnrpz, Implicit conservative schemes for the Euler equations, AIAA J, vol.24, issue.2, pp.2-5, 1986.